Answer:
It will charge 54.22 per hour to obtain a yield of 7.3% on the track dozer.
Explanation:
purchase cost 165,500
repair costing 26,000 at year 4
annual cost: 1,800 x 35 = 63,000
salvage value at end of useful life:
21% of purchase cost :
21% of 165,500 = 34,755
We will calculate the present value of the salvage value and the overhaul, to know how much does the company need to generate per year:
165,000 + pv of overhaul + pv of salvage value = present value of the cash inflow
pv of the overhaul
[tex]\frac{overhaul}{(1 + rate)^{time} } = PV[/tex]
overhaul: 26,000
time 4
rate 0.073
[tex]\frac{26000}{(1 + 0.073)^{4} } = PV[/tex]
PV $19,614.3744
Then, the PV of the salvage value:
[tex]\frac{salvage}{(1 + rate)^{time} } = PV[/tex]
salvage 34,755
time 6
rate 0.073
[tex]\frac{34755}{(1 + 0.073)^{6} } = PV[/tex]
PV $22,772.9326
165,500 + 19,614.3744-22,772.9326 = 163,341.4418
The present value of the contribution per hour at 7.3% discount rate should equal this amount
So we will set up the formula for the cuota of an annuity:
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV $163,341.44
time 6
rate 0.073
[tex]-34586.3538411519 \div \frac{1-(1+0.073)^{-6} }{0.073} = PV\\[/tex]
C 34,586.35
The contribution per year should be 34,586.35
each hour contribution should be: 34,586.35/1,800 = 19.2146
After the operating cost it should net 19.2146
hourly rate - 35 = 19.2146
hourly rate = 19.2146 + 35 = 54.2146 = 54.22
